Final Review PDF

Final Review Propositions/Predicates/Quantifiers Two or three questions Translation to/from English statements from/to logic expressions Scope of quantifiers, proposition vs predicate Nested quantifiers, negating quantifiers Logical Equivalence, Logical Reasoning One or two questions P...

Final Review Propositions/Predicates/Quantifiers Two or three questions Translation to/from English statements from/to logic expressions Scope of quantifiers, proposition vs predicate Nested quantifiers, negating quantifiers Logical Equivalence, Logical Reasoning One or two questions Proofs using truth tables/equivalence/inference rules Proof Methods One or two questions Direct proofs Proofs by contraposition/contradiction I suggest studying the examples/exercises in class, problems in the book, and homework problems. Your focus should be on how to start/setup a problem for a given method. Sets, Strings Three or four questions Definitions, examples Cardinality, subsets, set equality Cartesian product and strings Set operators Partitions Relations Two or three questions Relation Properties Reflexive Symmetric Antisymmetric Transitive Equivalence relation Partial Order Hasse Diagram Functions Two or three questions Domain, Codomain, Range Function Properties Injective Surjective Function Composition Floor, Ceiling functions Div and Mod Sequences, Summations Two or three questions Explicit formulars Sequences Recurrence relation Calculate the term at a given index. Which index did you use to calculate a given term? Calculate sum Mathematical Induction One proof question Understand base case Understand inductive hypothesis Be familiar with all parts required in proof Know the template required to write a proof by induction Counting Methods One or two questions Product rule Sum rule Permutation Combination Pigeonhole principle Graphs and trees Three or four questions Graph terminology Degree, neighborhood Special types of graphs Cycle, complete graphs Connected Components Chromatic numbers Graph coloring Trees Terminology Tree properties Finite Automata, Regular Expressions two or three questions Construct DFA/regular expression